If you have no idea what order she was in its going to be difficult to find out more.
Are there any other family members of the older generations still around? Do you have cousins/aunts/uncles who may have some information. Often different branches of the family know and remember different things.
If the family were catholic, you could try asking in their home parish, there may be something in the parish records or older parishioners who may remember her. Or contact the Diocese for the area, they too may hold information or be able to point you in the right direction. I'd start by getting a copy of that birth register entry, her d.o.b. may help an archivist at the Diocese.
I have been able to find information for two relatives who were nuns. For the first I knew the order and also her religious name and that she had spent a long time (including during WW2) in France. Originally I contacted the mother house to enquire if they were able to provide any information. They were very helpful and I got a lot of info from them. I also later managed to find an online database of those (prior to 1933) who took their vows in France which included my relative.
For the second, I had no idea that she had been a nun. I found her on an electoral register and noted that the address only had females listed. I searched the web and found that address was a convent/ teacher's training school.
I also found a death registration (which had her birth date on it) and then a burial record for her. The other occupants of the grave were also all female, so I contacted the cemetery dept and asked if they could tell me if the grave was maybe purchased by the order. Up to then I didn't know if she'd been a lay teacher who worked at a convent school or a member of the order.
Turned out the grave was purchased by the order so then I contacted the order who confirmed she had been a nun and very helpfully provided me with more info and also told me that someone else had enquired about the same lady and, if I wished, they would pass on my contact details to the other person. That, in turn, led to a lot more new information for me.
NB all the above took many years, tiny piece of info by tiny piece. Each little snippet I found eventually led me further, but it was a long and slow process.
The moral is, don't expect immediate results, but do keep poking round the records, ask anyone and everyone you can if they remember her and, if so, do they have any idea which order, where she may have been based, could they even describe the habit she wore etc etc. Any tiny bit could help with your search.
Good luck with it
Boo
